New improved convergence analysis for the secant method

被引：7
|
作者：
Alberto Magrenan, A. [1 ]
Argyros, Ioannis K. [2 ]
机构：
[1] Univ Int La Rioja, Dept Ordenac Docente, Logrono 26002, La Rioja, Spain
[2] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA
来源：
MATHEMATICS AND COMPUTERS IN SIMULATION | 2016年 / 119卷
关键词：
Secant method; Banach space; Majorizing sequence; Divided difference; Frechet-derivative; NEWTON-LIKE METHODS; SEMILOCAL CONVERGENCE; EQUATIONS;
D O I：
10.1016/j.matcom.2015.08.002
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
We present a new convergence analysis, for the secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz conditions in the convergence analysis. The new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies. Numerical examples validating the theoretical results are also provided in this study. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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页码：161 / 170
页数：10
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